Question: Expand and combine like terms. $(2x^3+4x^5)^2=$
Answer: We can expand this expression using the "perfect square" pattern (where $P$ and $Q$ can be any monomial): $(P+Q)^2=P^2+2PQ+Q^2$ $\begin{aligned} &\phantom{=}\left(2x^3+4x^5\right)^2 \\\\ &=\left(2x^3\right)^2+2\left(2x^3\right)\left(4x^5\right)+\left(4x^5\right)^2 \\\\ &=4x^6+16x^8+16x^{10} \\\\ &=16x^{10}+16x^8+4x^6 \end{aligned}$